Specific Latent Heat

Heat and Internal Energy

The temperature of a system is a measure of the kinetic energy of its particles. It only depends on how fast they are moving or vibrating. On the other hand, the system's potential energy depends on how the particles are bonded together, and thus it's related to the state of the system. When we heat a substance, we provide it with energy, but this can happen in two ways:

1. Increasing the temperature of the system. The particles comprising the system gain kinetic energy, moving faster and resulting in an increment of the system's temperature. This is what happens to the atoms of iron in a pan when it is heated on a stove, at the atomic level.

2. Changing the state of the system. The energy provided can also be used to break or change the bonds between the particles of the system. In general, this allows the particles to move farther apart, increasing the potential energy stored in the system and resulting in a new state. This is what usually happens when solids melt.

As the change of state occurs the potential energy of the particles increases.

Similarly, when the substance boils, the intermolecular bonds break again it becomes a gas. When a substance is in a gas state, its molecules try to stay away as much as possible from each other.

After a liquid becomes a gas, its particles tend to stay as far as possible from each other.

Keep in mind that in both cases, the internal energy increases as it is the sum of the kinetic and the potential energy. Therefore, as long as one of them increases, their sum increases as well. Now that we understand how, it is essential to understand when each of these energies increases as we heat our system:

• As long as the system remains in the same state, its potential energy will not change. Only the kinetic energy increases, and thus its temperature.

• When a change of state is occurring, all the energy is used to break or change the bonds between the particles of the system and increase their separation. Since the kinetic energy of the particles does not change, the temperature of the system remains constant during a change of state.

The graph below shows how the temperature of a kilogram of water changes as energy is provided.

When water is changing state, the temperature remains the same even if more energy is supplied. The flat lines represent this. On the other hand, when no state transition is occurring, the energy is used to increase the temperature of the water, as represented by the blue line segments with a positive gradient. Enrique Vizcarra Carrazco - StudySmarters Originals

Take a look at the middle part of the graph, where water is liquid. As energy is supplied, its temperature continues to increase until it reaches a critical value for the next state transition - vaporization. Even when the water has reached its boiling temperature,$100°\text{C}$, it still needs energy for the transition from liquid to gas to occur. This is why when we heat water to this temperature, it does all not become vapour at once. Moreover, once the water has reached$100°\text{C}$all energy is used to turn it into vapour, keeping the temperature constant.

Great! With all this information, we have a good understanding of how heat affects a system. We have already solved most of the questions at the begging this article, except for one: exactly how much energy is needed to make water boil? This can be answered by introducing the concept of specific latent heat.

Definition And The Formula for Specific Latent Heat

The specific latent heat changes from substance to substance. It can be determined experimentally using the following formula

$L=\frac{E}{m}$

$\text{specific latent heat =}\frac{\text{energy}}{\text{mass}}$

were$L$is the specific latent heat,$E$is the energy and$m$is the mass.

Specific Latent Heat Units

As indicated by the previous formula, the specific latent heat is obtained as the ratio of the energy needed for the state transition to the mass. Therefore, it has derived units obtained by dividing the units of energy by the units of mass. In the SI energy is measured in joules$\text{(J)}$and mass in kilograms$\text{(kg)}$. Hence the units for specific latent heat are

$\frac{\text{joules}}{\text{kilograms}}=\frac{\text{J}}{\text{kg}}$.

Specific Latent Heat Equation

If the specific latent heat and the mass of a substance are known, we can calculate the amount of heat needed for the change of state by using the specific latent heat equation with the energy isolated.

$E=Lm$

In the above equation,$E$is the energy in joules$\text{(J)}$, the specific latent heat$L$is in joules per kilogram$\left(\frac{\text{J}}{\text{kg}}\right)$, and$m$the mass is in kilograms$\text{(kg)}$. Considering the states: solid, liquid, and gas, we can have two different transitions. Therefore, we have two different values for the specific latent heat to consider.

Specific Latent Heat of Fusion

It is important to mention that the same amount of energy needs to be released by the system to go from liquid to solid. For example, the specific latent heat of fusion of water is$334,000\frac{\text{J}}{\text{kg}}$. This means that to melt one kilogram of ice we need to provide$334,000\text{J}$, but if we want to freeze a kilogram of water, we need to subtract$334,000\text{J}$from it instead.

The specific latent heat of fusion of water tells us how much energy we need to provide to melt a kilogram of ice. Conversely, we can freeze one kilogram of water by subtracting the same amount of energy from water. StudySmarter Originals

Recall that for the transition to occur, the substance has to be at its fusion temperature. The following table shows the specific latent heat of fusion for some substances.

You might be surprised to notice that water requires more energy to melt than most of the other substances shown. However, note that the specific latent heat of fusion has nothing to do with the fusion temperature! For example, to melt a kilogram of water, it is required around five times the energy to melt one kilogram of gold. However, the temperature at which water melts is$0°\text{C}$while gold melts at$1064°\text{C}$.

Specific Latent Heat of Vaporization

For a state change from gas to liquid, the energy should be subtracted from the substance instead of being added. The following table shows a few examples of substances and their specific latent heat of vaporization.